49 



complicated calculations which occur in the highest 

 application of Mathematics to physical problems. 

 By its aid it seems that an unskilled labourer may, in 

 a given time, perform the work of ten skilled arith- 

 meticians. The machine is applicable alike to the calcula- 

 tion of tidal, of magnetic, of meteorological, and perhaps 

 also of all other periodic phenomena. It will solve 

 differential equations of the second and perhaps of even 

 higher orders. And through the same invention the 

 problem of finding the free motions of any number of 

 mutually attracting particles, unrestricted by any of the 

 approximate suppositions required in the treatment of 

 the Lunar and Planetary Theories, is reduced to the 

 simple process of turning a handle. 



When Faraday had completed the experimental part 

 of a physical problem, and desired that it should thence- 

 forward be treated mathematically, he used irreverently 

 to say, " Hand it over to the calculators." But truth 

 is ever stranger than fiction ; and if he had lived until 

 our day, he might with perfect propriety have said, 

 " Hand it over to the machine." 



Had time permitted, the foregoing topics would have Mathematics 



,..,,, and obser- 



led me to pomt out that the mathematician, although vation. 

 concerned only with abstractions, uses many of the same 

 methods of research as are employed in other sciences, 

 and in the arts, such as observation, experiment, induc- 

 tion, imagination. But this is the less necessary because 

 the subject has been already handled very ably, although 

 with greater brevity than might have been wished, by 

 Professor Sylvester in his address to Section A. at our 

 meeting at Exeter. 



In an exhaustive treatment of my subject there would Origin of 



. ,. 1 . 1 • T , ii mathematical 



still remain a question which m one sense lies at the j^^eas. 

 bottom of all others, and which through almost all time 



